As a concrete example, consider that small-scale GBS devices made up of 3-mode interferometers, two PNR detectors registering up to 7 photons, and three momentum-squeezed vacuum states with up to \({12}{}\)  of squeezing have the potential of producing \(\mathinner {|{0^\Delta }\rangle }_{\rm gkp}\)  GKP states with \(\Delta ^2=0.1\)  (\(\Delta _{\text{dB}}={10}{}\)  , for \(\Delta =10^{-\Delta _{\text{dB}}/20}\) ) with a fidelity of 76% (92%, and 96%) and heralding success probability of 2.1% (0.4% and 0.1%) [1]}.
We see here a fidelity-probability trade-off for a fixed number of modes.
Comparable results are observed for the preparation of finite-energy GKP magic states.
